# Definition:Angle/Unit/Radian

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## Definition

The **radian** is a measure of plane angles symbolized either by the word $\radians$ or without any unit.

**Radians** are pure numbers, as they are ratios of lengths. The addition of $\radians$ is merely for clarification.

$1 \radians$ is the angle subtended at the center of a circle by an arc whose length is equal to the radius:

### Value of Radian in Degrees

The value of a radian in degrees is given by:

- $1 \radians = \dfrac {180 \degrees} {\pi} \approx 57.29577 \ 95130 \ 8232 \ldots \degrees$

This sequence is A072097 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

## Also see

## Technical Note

The $\LaTeX$ code for \(\radians\) is `\radians`

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## Sources

- 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $5$: Eternal Triangles: The origins of trigonometry

- For a video presentation of the contents of this page, visit the Khan Academy.